Problem: $J$ is the midpoint of $\overline{CT}$ $C$ $J$ $T$ If: $ CJ = 3x + 8$ and $ JT = 6x + 5$ Find $CT$.
Explanation: A midpoint divides a segment into two segments with equal lengths. ${CJ} = {JT}$ Substitute in the expressions that were given for each length: $ {3x + 8} = {6x + 5}$ Solve for $x$ $ -3x = -3$ $ x = 1$ Substitute $1$ for $x$ in the expressions that were given for $CJ$ and $JT$ $ CJ = 3({1}) + 8$ $ JT = 6({1}) + 5$ $ CJ = 3 + 8$ $ JT = 6 + 5$ $ CJ = 11$ $ JT = 11$ To find the length $CT$ , add the lengths ${CJ}$ and ${JT}$ $ CT = {CJ} + {JT}$ $ CT = {11} + {11}$ $ CT = 22$